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Excited state contamination is one of the most challenging sources ofsystematics to tackle in the determination of nucleon matrix elements and formfactors. The signal-to-noise problem prevents one from considering largesource-sink time separations for the three-point functions to ensure groundstate dominance. Instead, relevant analyses consider multi-state fits. Excitedstate contributions are particularly significant in the axial channel. In thiswork, we confront the problem directly. Since the major source of contaminationis understood to be related to pion production, we consider three-pointcorrelation functions with a nucleon operator at the source and a nucleon-pioninterpolating operator at the sink, which allows studies of $N \to N\pi$ matrixelements. We discuss the construction of these three-point correlationfunctions and we solve the generalized eigenvalue problem (GEVP) usingdifferent sets of nucleon and nucleon-pion interpolators. The analysis isperformed on the CLS ensemble A653 with $m_\pi \approx 420$ MeV. Results weregenerated with valence quark masses corresponding to $m_\pi \approx 1750$ MeVand $m_\pi \approx 420$ MeV.

Investigating $\mathbf{N \to N\pi}$ axial matrix elements